Bring a large pot of water to a boil. Season the pasta water generously with salt. Add the pasta and cook until it is al dente. Save ½ cup of the cooking liquid, drain the pasta, and set it aside.
While the pasta is cooking, in a large skillet over medium heat, add 1 pound ground beef. Cook, breaking up the large chunks of meat for about 4-5 minutes until it is no longer pink. Add the chopped onion and remaining spices, cooking until the onions are softened, about 5-6 minutes.
In a bowl, whisk together the Greek yogurt, minced garlic, lemon juice, and kosher salt. Taste and adjust seasoning as needed.
Before serving, melt the butter in a small saucepan and stir in the sweet paprika and red pepper flakes until bubbly.
In serving bowls, layer the cooked pasta, yogurt sauce, and beef. Drizzle with butter sauce and garnish with cherry tomatoes and mint or parsley.